The present invention pertains generally to dense plasma heating and more particularly to plasma heating by way of a relativistic electron beam.
Plasma heating has, for some time, been of great interest to the scientific community, since heated plasmas can be utilized for a wide variety of functions. A typical use of hot plasmas is the generation of energy in the form of radiation, neutrons, and alpha particles. Such an energy source can be useful in basic high-energy density plasma physics research, with practical application in scientific areas such as controlled thermonuclear fusion, material studies, and radiography.
Numerous techniques have been proposed in the prior art to produce dense, kilovolt plasmas. One of the more well-known techniques is the compression and heating of the core of a structured pellet by a laser or low-voltage electron beam. It has also been suggested that light- or heavy-ion beams could be utilized to obtain similar compression and heating. According to this technique, the structured pellet and its driving source are directly coupled through classical interactions by heating the outer layer of the structured pellet. Depending upon the characteristics of both the structured pellet and driving source, the outer layer explodes or ablates, leading to compression and heating of the core. Due to the direct coupling of all of these prior art driving sources, preheat of the core has been found to reduce the effectiveness of the compression, thereby reducing both density and temperature of the pellet core.
The use of a laser as a driving source in the above described confinement system has the added inherent disadvantages of low efficiency and associated high-development cost to produce lasers with the required power output for a directly driven structured pellet. Also, diffraction limitations and window damage thresholds make it difficult to focus proposed large lasers to millimeter diameters.
Low-impedance electron and light-ion beams also face expensive technological advancement to enable these beams to be focused to millimeter diameters, and to obtain power levels necessary to achieve the desired compression of the structured pellet. Low-impedance electron and light-ion sources are additionally limited in the manner of propagation of the beam to the pellet.
Heavy-ion sources also require significant technological advancement to produce the desired compression of the structured pellet. In fact, development of heavy-ion sources using conventional accelerator concepts appears to be considerably more expensive than the cost associated with the development of lasers. Beam propagation is also a limitation when employing heavy-ion sources.
High-density, kilovolt plasmas can also be produced by fast liners. Such devices can be driven by either magnetic forces or high expolsives, both of which lead to compression and heating of a confined plasma. Although both of these fast liner techniques have produced energy in the form of radiation, neutrons, and alpha particles, each technique has its own inherent disadvantage. The primary disadvantage of the high explosive driven liner is that the high explosives have a maximum power density of approximately 10.sup.10 watts/cm.sup.3 and a maximum detonation velocity of 8.8.times.10.sup.5 cm/sec, which limits achievable liner implosion velocity. Althrough useful in obtaining scientific data, such a system would be difficult to develop into a reuseable apparatus.
Magnetically driven liners are fabricated such that the liner forms part of the electrical discharge circuit in which current flowing through the liner creates a large magnetic field causing the liner to compress. Since the liner forms part of the electrical circuit, the external circuit resistance and finite liner resistivity lead to ohmic losses which lower the efficiency of converting electrical energy into liner kinetic energy. Also, since the liner must make electrical contact with the circuit, damage to the electrode connection between the moving liner and the electrode limits operability.
For liners which essentially remain thin solid shells during the implosion, ohmic heating and magnetic field diffusion limits implosion velocities to approximately 1 cm/.mu.sec. To obtain the desired radiation, neutron, and alpha particle output at such low implosion velocities, the plasma within the liner must be preionized and complex methods of overcoming heat conduction losses must be incorporated into the system.
Although liner implosion velocities exceeding 1 cm/.mu.sec can be achieved, ohmic heating and magnetic field diffusion converts solid liners into plasmas during operation. As a result, the thickness of the liner is increased, which lowers the potential for power multiplication. Even with very thin foils, implosion velocities are limited by the risetime of the driving current and diffusion of the driving magnetic field through the plasma liner.
Lasers have also been used to directly heat a magnetically confined plasma. According to this concept, a laser is used to heat a large volume of plasma confined by an elaborate magnetic field system to thermonuclear temperatures. Although the laser provides uniform ionization and rapid heating of a low-temperature plasma, the characteristic deposition length increases approximately as T.sub.3/2 for plasma electron temperatures T22 10 eV. This characteristic of the deposition of laser energy in the plasma, coupled with the large volume of plasma to be heated, places a total energy requirement for the laser which substantially exceeds present technology. Even if such lasers could be developed, the inherent low efficiencies associated with generation of laser energy would result in a large-capital investment for such a system.
A similar system incorporates a light- or heavy-ion beam to deposit its energy in a magnetically confined plasma. Since such beams are nonrelativistic, they exhibit a very low coupling efficiency and lack versatility obtainable by the relativistic interaction.
The concept of using an intense relativistic electron beam to heat a confined plasma has been investigated experimentally for a number of years. Prior art experiments have concentrated primarily on heating a large volume of plasma to thermonuclear temperatures with an electron beam, while maintaining the plasma with an external magnetic field. A typical configuration of a prior art experimental apparatus is shown in FIG. 1. A cathode 10 is positioned within a vacuum chamber 12 which is separated from the plasma chamber 14 by an anode foil 16. A series of dielectric spacers 18 are separated by a series of metal plates 20, which function together to prevent breakdown between the cathode 10 and the diode support structure 22. A solenoidal or mirror magnetic field configuration 24 is produced by an external source.
In operation, a relativistic electron beam 26 is formed by charging the cathode 10 with a fast risetime high-voltage pulse, causing electrons to be field emitted from the cathode 10 penetrating the anode foil 16 so as to enter the plasma chamber 14 as a relativistic electron beam 26. As the relativistic beam propagates through the plasma along the externally applied axial magnetic field 24, the plasma is heated by the following methods:
(a) relaxation heating due to relativistic streaming instabilities (two-stream and upper-hybrid bunching instabilities); and,
(b) amomalous resistive heating due to the presence of a plasma return current (ion-acoustic and ion-cyclotron instabilities).
Typically, devices such as klystrons, magnetrons, vacuum tubes, etc., which are based upon electron bunching according to method (a) have been considered very efficient devices with respect to energy utilization. Therefore, the process of heating a plasma by electron bunching, i.e., by generating the two-stream and upper-hybrid instabilities according to method (a), was initially expected to be an efficient technique for producing a thermonuclear plasma. Although all early experiments observed anomalous (nonclassical) coupling of the beam energy to the plasma resulting from the presence of the streaming instabilities according to the method (a), the coupling efficiency was only on the order of 15% at plasma densities of approximately 10.sup.12 electrons/cm.sup.3, and dropped rapidly to less than a few percent as the plasma density approached 10.sup.14 electrons/cm.sup.3. These results were obtained with anode foils having thicknesses on the order of 25 .mu.m to 50 .mu.m and conventional electron beams available for experiments during this period which typically had relatively low voltages, i.e., 1 MeV or less. This combination of relatively thick anode foils and low-voltage beams resulted in classical anode foil scattering of the beam which prevented the relativistic streaming instabilities from efficiently coupling the beam energy to the plasma. In other words, although unknown to the experimentalists and theoreticians during the period 1970-1975, the foil thickness and low voltage of the electron beams used in the experiments caused the electron beam to scatter in a manner which prevented substantial electron bunching in the beam. This, in turn, produced the observed rapidly decreasing energy absorption efficiencies as the plasma density approached 10.sup.14 electrons/cm.sup.3. As a result of these low observed efficiencies, scientific attention shifted toward investigation of the resistive heating mechanism according to method (b), which was known to have several scientifically interesting properties.
One property of the resistive heating mechanism of method (b) is its ability to place a substantial fraction of the beam energy into plasma ions. This differs from the streaming instabilities which primarily heat the plasma electrons. Since the ions must eventually be heated in a magnetically contained plasma, according to conventional magnetic confinement systems, direct heating of the ions eliminates an energy conversion step. Furthermore, when energy is initially deposited into plasma electrons rather than the ions, heat conduction is enhanced due to the initially elevated electron temperature, so that achievable plasma confinement time is shortened. Consequently, increased magnetic field strengths are required to produce comparable confinement.
Another property of the resistive heating mechanism is its ability to heat a large volume of plasma in a uniform manner, rather than depositing energy in a small localized region, as is characteristic of the optimized streaming instability mechanism. The ability to directly heat a large volume of plasma in a uniform manner by resistive heating thus avoids problems of heat redistribution within the plasma. Moreover, the potential for developing a plasma heating system which could also be used in conjunction with devices requiring preheated plasmas, such as tokamaks which has received substantial funding, renders the resistive heating mechanism even more attractive. For these reasons, experimental attention was directed from the onset of plasma heating experiments using relativistic electron beams towards producing resistive heating in plasmas according to method (b). Consequently, experimental apparatus to optimize resistive heating effects, such as low-voltage electron beams with high .nu./.gamma. outputs, were utilized in ongoing experiments of relativistic electron beam heated plasmas. Here, .gamma. is the beam relativistic factor which is nearly proportional to the beam particle voltage. The ratio .nu./.gamma. is basically a measure of the beam self-magnetic field energy to beam particle energy. The increased use of high .nu./.gamma. beams is more graphically shown in FIGS. 2 and 3 which illustrate the decrease in maximum beam voltage and increase in maximum .nu./.gamma. for relativistic electron beam experiments between 1970 and 1975. Thus the prior art experiments have, from the beginning, concentrated on high .nu./.gamma., low-voltage beams for optimizing the resistive heating mechanism according to method (b), virtually ignoring the effect of streaming instabilities produced according to method (a).
In so doing, prior art experiments, have clearly pointed out the limitations of resistive heating according to method (b), i.e., that resistive heating does not scale to higher density plasmas, but, to the contrary, is absolutely limited by self-stabilization within the plasma. More particularly, the experiments have shown that above a certain electron temperature, depending on the density of the plasma, low-frequency instabilities which are responsible for resistive heating, are stabilized. Consequently, only classical resistivity, which is inadequate to couple significant energy to the plasma from the relativistic electron beam, has any effect in resistively heating the plasma.
In addition to this inherent stabilization limitation, the technique of resistive heating has several other disadvantages. First, even if experiments had shown that resistive heating according to method (b) was effective at high plasma density, the required .nu./.gamma. for efficient coupling would be at least an order-of-magnitude higher than that achievable by present day technology. Second, since resistive heating is only suitable for low plasma densities which are very large in volume, the total energy required to heat such a plasma would again, be at least an order-of-magnitude beyond the total beam energy achievable by present technology standards.
As a result of these limitations, and the belief by prior art theoreticians and experimentalists that resistive heating dominated anomalous energy deposition in plasmas, the relativistic electron beam plasma heating program in the United States was virtually abolished in 1975 without any further investigation into the streaming instability heating mechanism.